Why does this question receive so much attention, and why do people give essentially the same answer over and over!
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MBNMar 15 '11 at 16:22

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Everything was said, but not by everybody. The credo of people too lazy to read the thread before writing.
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GeorgMar 15 '11 at 20:14

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How can a question that generates so many answers get a negative vote?
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Carl BrannenMar 16 '11 at 2:11

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-1. @Vinoth this question is ill-formed, to say the least. You provide no context or motivation or some idea of your background so one knows how to respond and at what level. @Carl this is the sort of question that, because it is ill-defined, becomes a Rorschach-test with people providing answers for what they interpret the question to be. Is this really the standard we want to set for questions on this site?
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user346Mar 16 '11 at 2:56

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-1 I am really sorry for down voting, but I don't think that this question is appropriate for this site. Maybe you should check out physicsforums.com for other questions of this sort. Personally I would be more interested and active on this site if the level of questions were on advanced graduate to research level, and I think many more competent people would join in.
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HeidarMar 24 '11 at 23:56

6 Answers
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The answers given so far are fine, but to my surprise nobody's mentioned the most important point: in modern terminology, we generally don't say that the mass of an object increases with speed. "Relativistic mass increase" is outdated terminology, not used by most physicists anymore. In general, nowadays, "mass" means "rest mass" and is independent of velocity. Igor Ivanov's answer to this question says it all.

I haven't read the article by Lev Okun that he refers to, but I like the term "pedagogical virus" for this notion.

It means that its inertia (resistance to change in the state of motion) approaches infinity. You probably already know from $F=ma$ that for the same change in speed (acceleration), a larger mass requires a larger force. As the velocity of a body approaches the speed of light, its inertia (i.e. $\gamma m$) becomes so high that you need an impossibly infinite force to accelerate it to exactly the speed of light.

And as Georg says, whenever you see "becomes infinite", read it as "approaches infinity".

It means that if a finite force acts on the mass in its stationary frame, then in all other frames as the measured velocity approaches c, the acceleration approaches 0 which implies the "relativistic mass", the "apparent mass" the "effective mass", call it what you will, approaches infinity.

If you want to imagine an infinite mass just think of a piece of matter which does not response (i.e. accelerate) to any force. Obviously, it is an ideal concept. In reality "the mass approaching infinity" means it is increasing without any finite upper limit.

The mass will never be infinite because it would require infinite work to reach required speed. It's just a figure of speech.

Instead of trying to imagine "infinite mass" try imagining the process: as you apply force ("press the accelerator pedal") the object instead of going faster, gets heavier. The more work you provide, the heavier the object gets.

Wasn't there enogh written on "rechurners" in the comments? -1
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GeorgMar 25 '11 at 13:01

@Georg: Where in the other comments was work-mass correlation mentioned? It is deceivingly easy to think "something suddenly becomes infinitely heavy" and ponder how that happens. If every gram of weight gained means 90 terajoules of energy expended, it opens eyes on cost of "going to infinity".
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SF.Mar 25 '11 at 13:44

So on top You did not understand the question at all.
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GeorgMar 25 '11 at 14:04

If that is so, then I still don't. Care to explain?
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SF.Mar 25 '11 at 15:07